Question: Express this quotient in scientific notation: ${\frac{1.680\times 10^{-1}} {7.0\times 10^{-5}}}$
Solution: Start by collecting like terms together. $= {\frac{1.680} {7.0}} \times{\frac{10^{-1}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.24 \times 10^{-1\,-\,-5}$ $= 0.24 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.24$ is the same as $2.40 \div 10$ , or $2.40 \times 10^{-1}$ $ = {2.40 \times 10^{-1}} \times 10^{4} $ $= 2.40\times 10^{3}$